Incidentally, one tip is to look for simplifications you can make at every step of the problem; for example, before doing anything, notice that the denominator of both sides is divisible by 7; you could multiply the equation through by 7 to cancel that out and reduce the size of the numbers with which you have to work.

When you perform a noninvertable operation to an equation, it says "The solution(s) to the original equation is (are) among the solutions to this new equation". Generally it's good practice to check your solutions when you get them, but it becomes a necessity when you use noninvertable operations like squaring.

In many types of problems where there squaring introduces "false" solutions, the false solutions correspond to some sort of reversal of sign or direction. In this particular case, it corresponds to the case when cos &theta; = -4/21